South Australian independent Senator Nick Xenophon says it's almost "Keystone Cops stuff" that police have yet to seek the extradition from Fiji of alleged doomsday cult leader Rocco Leo.

Leo was arrested in Fiji last month for visa breaches, along with his closest associates Marie Veneziano and her brother Joseph.

Rocco Leo is facing 126 charges for fraud

He fled Australia last year just before SA police raided several of his Agape Ministries' properties in Adelaide, seizing guns, detonators and 35,000 rounds of ammunition.

Police have a warrant out for his arrest alleging 126 counts of fraud while he also faces civil action from two former followers who say they were tricked into giving him more than $1.5 million.

Senator Xenophon said on Tuesday that it was up to SA authorities to seek Leo's extradition from Fiji but he had been told that no request was likely to be made.

He released letters he had received from and Home Affairs Minister Brendan O'Connor and Fiji's Prime Minister Commodore Frank Bainimarama.

Cdre Bainimarama told Senator Xenophon that Fiji would assist with any application for extradition but that no request had come from the federal government.

While Mr O'Connor said it was up to SA authorities to ask for the extradition.

"I understand that it is not currently the intention of South Australian authorities to seek the extradition of Mr Leo," the minister said in his letter.

Senator Xenophon said it beggared belief that a man facing criminal charges was not being brought to justice because South Australian authorities had not yet called for his extradition.

"This is almost Keystone Korps stuff," he said.

"Rocco Leo is facing 126 charges for fraud in this state and the government should be calling for his return," he said.

"The ball is well and truly in the South Australian government's court."

SA police (SAPOL) said Leo remained in custody and faced possible deportation from Fiji.

But they said deportation and extradition were distinct processes.

"Any decision to deport a person is solely a matter for that foreign country," Assistant Commissioner Grant Stevens said in a statement.

"Deportation is not an alternative to extradition. No bilateral extradition treaty exits between Australia and Fiji and as such SAPOL continues to consult with both state and commonwealth attorneys-general on this issue.

"If Fiji does deport Mr Leo to an Australian port other than South Australia, SAPOL will apply for extradition so that he can be returned to this state to face court."

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